Computational geometry: an introduction
Computational geometry: an introduction
Obstacle growing in a nonpolygonal world
Information Processing Letters
Efficient Parallel Convex Hull Algorithms
IEEE Transactions on Computers
IEEE Transactions on Computers
Journal of Parallel and Distributed Computing
Parallel computational geometry
Parallel computational geometry
Parallel Computations on Reconfigurable Meshes
IEEE Transactions on Computers
Reconfigurable Buses with Shift Switching: Concepts and Applications
IEEE Transactions on Parallel and Distributed Systems
Constant-time convexity problems on reconfigurable meshes
Journal of Parallel and Distributed Computing
Constant Time Algorithms for Computational Geometry on the Reconfigurable Mesh
IEEE Transactions on Parallel and Distributed Systems
An Efficient Algorithm for Row Minima Computations on Basic Reconfigurable Meshes
IEEE Transactions on Parallel and Distributed Systems
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
Computer Vision
IEEE Transactions on Parallel and Distributed Systems
A Fast Parallel Algorithm for Convex Hull Problem of Multi-Leveled Images
Journal of Intelligent and Robotic Systems
Journal of Intelligent and Robotic Systems
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The problem of computing the convex hull of a set of n sorted points in the plane is one of the fundamental tasks in image processing, pattern recognition, cellular network design, and robotics, among many others. Somewhat surprisingly, in spite of a great deal of effort, the best previously known algorithm to solve this problem on a reconfigurable mesh of size $\sqrt n\times \sqrt n$ was running in O(log2n) time. It was open for more than ten years to obtain an algorithm for this important problem running in sublogarithmic time. Our main contribution is to provide the first breakthrough: We propose an almost optimal convex hull algorithm running in O((log log n)2) time on a reconfigurable mesh of size $\sqrt n\times \sqrt n.$ With slight modifications, this algorithm can be implemented to run in O((log log n)2) time on a reconfigurable mesh of size ${\textstyle{{\sqrt n} \over {{\rm log\,log}\,n}}}\times {\textstyle{{\sqrt n} \over {{\rm log \,log}\,n}}}.$ Clearly, the latter algorithm is work-optimal. We also show that any algorithm that computes the convex hull of a set of n sorted points on an n-processor reconfigurable mesh must take 驴(log log n) time. Our result opens the door to an entire slew of efficient convex-hull-based algorithms on reconfigurable meshes.